100,000 is 100 thousands, so we have an inequality

74.5 + 43.75*sin(pi*t/6) > 100. Solve for sin:

sin(pi*t/6) > (100-74.5)/43.75 = 0,582857...

pi*t/6 is >0 and <=2pi (t = 1..12). Looking at the sin's graph we understand that pi*t/6 must be between

arcsin(0,582857) and pi-arcsin(0,582857) which is 0,62... and 2.52, or

arcsin(0,582857)*6/pi < t < (pi-arcsin(0,582857))*6/pi or

1.11 < t < 4.81.

So t=2, 3, 4.

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